SAR成像RD算法MATLAB仿真_用matlab软件对rd算法成像进行仿真;用matlab软件处理实测数据得到最终的雷达成像

SAR成像RD算法MATLAB仿真

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SAR imaging: RD_algorithm
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear; clc;
close all;
%%%%%% 参数设置
%%%%%%%%%%%%%%% constant parameters %%%%%%%%%%%%%%%%%%%

c = 3e8; % speed of light,3*10^8m/s

%%%%%%%%%%%%%%% chirp signal parameters %%%%%%%%%%%%%%%

fc = 3e9; % carrier frequency,**GHz
wc = 2 * pi * fc;
lambda = c / fc; % Wavelength at carrier frequency
Tr = 1.5e-6; % chirp pusle duration 1.5us
Br = 150e6; % chirp frequebcy bandwidth 150Mhz
Kr = Br/Tr; % chirp signal: frequency modulation rate

%%%%%%%%%%%%%% observating strip parameters %%%%%%%%%%%%

H = 3000; % 飞行平台的高度
ThetaCenter = 45 / 180 * pi; % 正侧视SAR系统的斜视角
Platform_center = [0, 0, H]; % 飞行平台的位置坐标

Y_C = H * tan(ThetaCenter);
Scene_center = [0, Y_C, 0]; % 场景中心的位置坐标
delta_X = 150; % 场景区域的范围：x坐标（平台飞行方向）
delta_Y = 100; % 场景区域的范围：y坐标
Xmin = -delta_X / 2;
Xmax = delta_X / 2;
Ymin = -delta_Y / 2;
Ymax = delta_Y / 2;
RC0 = sqrt(sum((Scene_center - Platform_center) .^2)); %天线平台中心到场景中心的距离

%%%%%%%%%%%%%% performance parameters %%%%%%%%%%%%%%%%%%

rho_R = c / (2 * Br); % 距离分辨率（m）
roh_Y = rho_R / sin(ThetaCenter); % 透视矫正后的切航迹向(CT)分辨率（m）
rho_AT = rho_R; % 沿航迹向(AT)的理论分辨率（m）

V = 150; % 飞行平台的速度（x轴：m/s）
D = 2 * rho_AT; % 沿航迹向的实天线孔径长度，page 63, function(3.27)
Lsar = lambda * RC0 / D; % AT向一个合成孔径的长度; page 59, function(3.14)
Tsar = Lsar / V; % 一个合成孔径时间

%%%%% fast-time sampling sequence

Rate_Fs = 1.2; % 快时间域的过采样系数为1.2
Fs = round(Rate_Fs * Br); % 距离维的过采样率（双通道：实部＝I， 虚部＝Q）
Ts = 1 / Fs; % 快时间采样时间间隔
delta_Rs = Ts * c; % 快时间采样间隔对应的距离长度

Rmin = sqrt((Y_C + Ymin)^2 + H^2); % 场景最短距离
Rmax = sqrt((Y_C + Ymax)^2 + (Lsar/2)^2 + H^2); % 场景最大距离
Nfast = ceil((2 * (Rmax-Rmin) / c + Tr) / Ts); % 距离向的采样点个数
Nf = 2^nextpow2(Nfast); % for fft
tf_org = [-Nf/2 : (Nf/2 - 1)] * Ts; % 理想快时间采样序列
% tff = tf_org*c;
% tr_ff = (tff/2 + RC0) / sin(pi/4);
tf = (2 * RC0 / c) + tf_org; % 实际快时间采样值
tr = tf * c / 2; % 快时间采样对应的距离域(单程距)

%%%%% slow-time sampling sequence

Ka = -2 * V^2 / (lambda * RC0); % 多普勒调频率,(美SAR，p159, func(6.5))
Ba = abs(Ka * Tsar); % 多普勒带宽
Rate_PRF = 1.25; % 慢时间域的过采样系数为1.25
PRF = round(Rate_PRF * Ba); % 脉冲重复频率
PRT = 1 / PRF; % 脉冲重复周期,（一个脉冲重复周期内，飞机的飞行时间间隔）

Nslow = ceil((delta_X + Lsar) / V / PRT); % 方位向采样点个数
Ns = 2^nextpow2(Nslow); % 优化采样点数（for fft）
% Ns = Nslow;
ts = [-Ns/2 : (Ns/2 - 1)] * PRT; % 慢时间采样序列
ta = ts * V; % 慢时间采样对应的距离域

%%%%%
% % delta_d_AT = lambda; % AT向的阵元间隔（由SAR原理形成）
% % PRF = round(V / delta_d_AT); % 脉冲重复频率
% % p = nextpow2(A) returns the smallest power of two that is greater than or equal to the absolute value of A.
% X_start = Xmin - Lsar/2; % 场景范围：x轴最小值
% X_end = Xmax + Lsar/2; % 场景范围：x轴最大值
% ts = linspace(X_start / V, X_end / V, Ns); % 对方位向时间采样
% % temp_ts = diff(ts);
% % PRT = sum(temp_ts(?) / length(temp_ts); % 离散化脉冲重复周期
% dts = ts(2) - ts(1); % 离散化脉冲重复周期
% Fsa = 1/dts; % 脉冲重复周期
% delta_d_AT = V * Fsa; % AT向的阵元间隔

%%%%%%%%%%%%% SAR　Resolution %%%%%%%%%%%%%%%%%%%%%%%%%

% Dr=c/2/Br; % range resolution
% Dx=v/Ba; % cross-range resolution

%%%%%%%%%%%% set point targets parameters %%%%%%%%%%%%%%%

% format [x, y, z, RCS]
Ptargets = [ 0, 0, 0, 1 %];
-20, 0 0, 1
50, 0 0, 1
0, 20, 0, 1]; % 定义点目标的相对位置及兵役散射系数

Ntar = size(Ptargets, 1); % 点目标个数
Ptargets(:, 1:3) = Ptargets(:, 1 : 3) + ones(Ntar, 1) * Scene_center; % 点目标的真实坐标位置

%%%%%%%%%%%%%%%%%%% Show the targets %%%%%%%%%%%%%%%%%%%

figure, plot(Ptargets(:, 1), Ptargets(:, 2), ‘o’,‘MarkerEdgeColor’,‘b’,‘MarkerFaceColor’,‘g’); %, ‘MarkerSize’, 12
grid on
% axis equal;
axis([Scene_center(1)+Xmin Scene_center(1)+Xmax Scene_center(2)+Ymin Scene_center(2)+Ymax]);
xlabel(‘x轴(AT向)’);
ylabel(‘y轴(CT向)’);
title(‘观测场景及点目标’)

%=%
%=%

disp(’*********************************************************’);
fprintf(1,‘系统参数显示界面：\n’);
fprintf(1,’\n’);
disp([‘快时间域采样点数是:’, poly2str(Nf)]);
disp([‘快时间域的过采样率是:’, poly2str(Rate_Fs)]);

disp([‘PRF:’, poly2str(PRF)]);
disp([‘慢时间域采样点数是:’, poly2str(Ns)]);
disp([‘慢时间域的过采样率是:’, poly2str(Rate_PRF)]);

disp([‘AT向合成孔径的长度是:’, poly2str(Lsar), ’ m’]);
disp([‘距离向的分辨率是:’, poly2str(rho_R), ’ m’]);
disp([‘沿航向的分辨率是:’, poly2str(rho_AT), ’ m’]);
fprintf(1,’\n’);
disp(’*********************************************************’);

%=%
%=%

%%%%%%%%%%%%%% Generate the raw signal data %%%%%%%%%%%%%%%%%%%

Echo_data = zeros(Ns, Nf); % 初始化回波数据域
for ii = 1 : Ntar
sigma = Ptargets(ii, 4); % 获取反射系数
Xslow = ts .* V - Ptargets(ii, 1); % 雷达在慢时域的移动距离，Xslow为1×Ns的矩阵
Yslow = Platform_center(2) - Ptargets(ii, 2);
Zslow = Platform_center(3) - Ptargets(ii, 3);
R = sqrt(Xslow.^2 + Yslow^2 + Zslow^2); % 雷达与目标的距离
tau = 2 * R / c; % 信号走双程的总延时，tau为1N的矩阵
Dfast = ones(Ns,1) * tf - tau’ * ones(1, Nf); % 雷达相对目标移动在快时域产生的时间差，tm为1M的矩阵，Dfast就为NM的矩阵
phase = piKrDfast.^2 - (4 * pi / lambda * R’) * ones(1,Nf); % 第一项是指信号走双程的总延时所带来的相位延迟，第二项指双程距离R所带来的相位延迟
Echo_data = Echo_data + sigma * exp(jphase) .* (abs(Dfast) <= Tr/2) .* ((abs(Xslow) <= Lsar/2)’ * ones(1,Nf));
end

%%%%%%%%%%%%%%%%% Range compression %%%%%%%%%%%%%%%%%%%%%%

%%%%% 窗函数
% WinTr = (abs(tf_org) <= Tr/2);
% WinIndex = find(WinTr ~= 0);
% WinLength = length(WinIndex);
% WinStart = min(WinIndex(?);
% WinEnd = max(WinIndex(?);
% WindowTr = zeros(size(tf));
% WindowTr(1, WinStart : WinEnd) = hamming(WinLength).’;
% % figure,plot(WindowTr);
% h_ref = exp(j * pi * Kr * tf_org.^2) .* WindowTr; % 距离向参考函数,时域

h_ref = exp(j * pi * Kr * tf_org.^2) .* (abs(tf_org) <= Tr/2); % 距离向参考函数,时域
h_ref = h_ref .* (hamming(Nf).’); % 加窗后的参考函数
H_ref = fty(ones(Ns, 1) * h_ref);
% figure, plot(abs(H_ref(2, ?));
% title(‘参考函数的频谱’);

Comp_f = fty(Echo_data) .* conj(H_ref); % 距离压缩的频域形式
Comp_tsf = ifty(Comp_f); % 距离压缩的“快时间-慢时间”域形式（ts-tf）
Comp_Rfd = ftx(Comp_tsf); % Azimuth FFT and Range-Doppler domain (fd-tf)
% figure, plot(abs(Comp_tsf(Ns/2, ?));
% title(‘距离压缩后的数据抽检’);

%%%%%%%%%%%%% 距离弯曲（徙动）校正 – RCMC %%%%%%%%%%%%%%%%%%

fd_r = [-Nf/2 : (Nf/2 - 1)] * Fs / Nf;
FF = ones(Ns, 1) * fd_r; % FF为N*M的矩阵
fdc = 0; % doppler center
fd_a = [-Ns/2 : (Ns/2 - 1)] * PRF / Ns;
FU = fd_a.’ * ones(1, Nf);
Refcorr = exp(j * pi / fc^2 / Ka * (FU.FF).^2 + j * pi * fdc^2 / fc / Ka * FF - j * pi / fc / Ka * FU.^2 . FF); % Range-Doppler domain

%RCMC function

RanComff=ftx(Comp_f); % FFT in Azimuth
RanComffcorr=RanComff .* Refcorr; % RCMC
RanComtfcorr=ifty(RanComffcorr); % data in Range_Doppler domain
RanComttcorr=iftx(RanComtfcorr); % data in Range_Azimuth domain

%%Azimuth compression
ts_mid = ts - 0/V; % 与场景参考点的慢时域时间差
Refa = exp(j * pi * Ka * ts_mid.^2) .* (abs(ts_mid) < Tsar/2); % 方位压缩参考函数
Sa = iftx(Comp_Rfd .* (conj(ftx(Refa)).’ * ones(1, Nf))); % 未进行距离徙动校正后的距离方位压缩结果
Sa_RCMC = iftx(ftx(RanComttcorr).*(conj(ftx(Refa)).’*ones(1, Nf))); % 对距离徙动校正后的距离方位压缩结果

%%%%%%%%%%%%%%%%%%% 成像过程中的图像显示 %%%%%%%%%%%%%%%%%%%%%
% %%%% 01 原始回波数据
% figure,
% G = 20 * log10(abs(Echo_data)); % 换算成分贝（dB）的形式显示
% gm = max(max(G));
% thr01 = 40; % 显示的动态范围40dB,“thr” = threshold
% g_thr = gm - thr01;
% G = (G - g_thr) * (255 / thr01) .* (G > g_thr);
% imagesc(tr, ta, -G); % 显示原始回波数据图像
% colormap(gray); % 使显示的图像为灰度图像
% grid on,axis tight,
% xlabel(‘Range’)
% ylabel(‘Azimuth’)
% title([’(a)原始信号, 场景中心的单程距为：Rc = ‘, num2str(RC0), ‘m’])
%
%%%% 02 距离压缩后数据（未进行 RCMC 前）
figure,
G = 20 * log10(abs(Comp_tsf)); % 换算成分贝（dB）的形式显示
gm = max(max(G));
thr02 = 40; % 显示的动态范围40dB,“thr” = threshold
g_thr = gm - thr02;
G = (G - g_thr) * (255 / thr02) .* (G > g_thr);
imagesc(tr, ta, -G);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘Range’)
ylabel(‘Azimuth’)
title([’(b)距离压缩后的时域信号, Rc = ', num2str(RC0), ‘m’])

%%%% 03 距离压缩后距离多普勒域（未进行 RCMC 前）
figure,
G = 20 * log10(abs(Comp_Rfd)); % 换算成分贝（dB）的形式显示
gm = max(max(G));
thr03 = 40; % 显示的动态范围40dB,“thr” = threshold
g_thr = gm - thr03;
G = (G - g_thr) * (255 / thr03) .* (G > g_thr);
imagesc(tr, fd_a, -G);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘Range’)
ylabel(‘Doppler’)
title(‘RCMC前：Range Doppler domain’)

%%%% 04 RCMC后: 距离压缩后距离多普勒域
figure,
G = 20 * log10(abs(RanComtfcorr)); % 换算成分贝（dB）的形式显示
gm = max(max(G));
thr04 = 40; % 显示的动态范围40dB,“thr” = threshold
g_thr = gm - thr04;
G = (G - g_thr) * (255 / thr04) .* (G > g_thr);
imagesc(tr, fd_a, -G);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘Range’)
ylabel(‘Doppler’)
title(‘RCMC后：Range Doppler domain’)

%%%% 05 未进行距离徙动校正后的距离方位压缩结果
figure,
G = 20 * log10(abs(Sa)); % 换算成分贝（dB）的形式显示
gm = max(max(G));
thr05 = 40; % 显示的动态范围40dB,“thr” = threshold
g_thr = gm - thr05;
G = (G - g_thr) * (255 / thr05) .* (G > g_thr);
imagesc(tr, ta, -G);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘Range’)
ylabel(‘Doppler’)
title(‘05 未进行距离徙动校正后的距离方位压缩结果’)

%%%% 06 未进行距离徙动校正后的距离方位压缩结果
figure,
G = 20 * log10(abs(Sa_RCMC)); % 换算成分贝（dB）的形式显示
gm = max(max(G));
thr06 = 40; % 显示的动态范围40dB,“thr” = threshold
g_thr = gm - thr06;
G = (G - g_thr) * (255 / thr06) .* (G > g_thr);
imagesc(tr, ta, -G);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘Range’)
ylabel(‘Doppler’)
title(['06 对距离徙动校正后的距离方位压缩结果, Rc = ', num2str(RC0), ‘m’]);

%%%% 07 透视校正后的最终结果
figure,
% tr_rectify = sqrt((tr).^2 - H.^2);
% tr_rectify = Y_C + (tr-RC0) ./ sin(acos(H./(tr)));
tr_rectify = Y_C + (tr-RC0) ./ sin(ThetaCenter);
imagesc(ta, tr_rectify, -G.’);
% imagesc( -G.’);
colormap(gray); % 使显示的图像为灰度图像
grid on,axis tight,
xlabel(‘x轴：AT向’)
ylabel(‘y轴：CT向’)
title(['07 透视校正后的最终结果, Y0 = ', num2str(Y_C), ‘m’]);

---

用到的子函数：
function fs=ftx(s);
fs=fftshift(fft(fftshift(s)));

function fs=fty(s);
fs=fftshift(fft(fftshift(s.’))).’;

function s=iftx(fs);
s=fftshift(ifft(fftshift(fs)));

function s=ifty(fs);
s=fftshift(ifft(fftshift(fs.’))).’;